Initial commit: Build project architecture, define interfaces, write documentation, with the help of Claude

74 files changed, 3476 insertions, 0 deletions

diff --git a/.cache/clangd/index/clausifier.cpp.9FD5A8E503FCC1D9.idx b/.cache/clangd/index/clausifier.cpp.9FD5A8E503FCC1D9.idx
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diff --git a/.cache/clangd/index/discrim_tree.cpp.E42DE863D5277544.idx b/.cache/clangd/index/discrim_tree.cpp.E42DE863D5277544.idx
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diff --git a/.cache/clangd/index/main.cpp.E859CA8999ADDE12.idx b/.cache/clangd/index/main.cpp.E859CA8999ADDE12.idx
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diff --git a/.cache/clangd/index/proof_trace.cpp.1C59D7C4E2AA6F75.idx b/.cache/clangd/index/proof_trace.cpp.1C59D7C4E2AA6F75.idx
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diff --git a/.cache/clangd/index/prover.cpp.3C0A611D8081F4D2.idx b/.cache/clangd/index/prover.cpp.3C0A611D8081F4D2.idx
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diff --git a/.cache/clangd/index/resolution.cpp.DB2A5A3C44A70C4B.idx b/.cache/clangd/index/resolution.cpp.DB2A5A3C44A70C4B.idx
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diff --git a/.cache/clangd/index/subsumption.cpp.6D5F5B98AE9124E8.idx b/.cache/clangd/index/subsumption.cpp.6D5F5B98AE9124E8.idx
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diff --git a/.cache/clangd/index/symbol_table.cpp.685747B6B16C64EF.idx b/.cache/clangd/index/symbol_table.cpp.685747B6B16C64EF.idx
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diff --git a/.cache/clangd/index/term_bank.cpp.943AA1306E763CC8.idx b/.cache/clangd/index/term_bank.cpp.943AA1306E763CC8.idx
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diff --git a/.cache/clangd/index/test_clausifier.cpp.FF3EDB07B9DFBBC1.idx b/.cache/clangd/index/test_clausifier.cpp.FF3EDB07B9DFBBC1.idx
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diff --git a/.cache/clangd/index/test_discrim_tree.cpp.9508FB8B5A477D10.idx b/.cache/clangd/index/test_discrim_tree.cpp.9508FB8B5A477D10.idx
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diff --git a/.cache/clangd/index/test_prover.cpp.604919AAC374F32C.idx b/.cache/clangd/index/test_prover.cpp.604919AAC374F32C.idx
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diff --git a/.cache/clangd/index/test_resolution.cpp.E785AA54A14F55A5.idx b/.cache/clangd/index/test_resolution.cpp.E785AA54A14F55A5.idx
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diff --git a/.cache/clangd/index/test_term_bank.cpp.50AF7E4F3359B770.idx b/.cache/clangd/index/test_term_bank.cpp.50AF7E4F3359B770.idx
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diff --git a/.cache/clangd/index/test_unification.cpp.BA63AEE14AACBCCC.idx b/.cache/clangd/index/test_unification.cpp.BA63AEE14AACBCCC.idx
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+++ b/.cache/clangd/index/test_unification.cpp.BA63AEE14AACBCCC.idx
diff --git a/.cache/clangd/index/tptp_parser.cpp.50E69F3F47D54605.idx b/.cache/clangd/index/tptp_parser.cpp.50E69F3F47D54605.idx
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--- /dev/null
+++ b/.cache/clangd/index/tptp_parser.cpp.50E69F3F47D54605.idx
diff --git a/.cache/clangd/index/unification.cpp.FAE8F2832CAC7DB0.idx b/.cache/clangd/index/unification.cpp.FAE8F2832CAC7DB0.idx
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--- /dev/null
+++ b/.cache/clangd/index/unification.cpp.FAE8F2832CAC7DB0.idx
diff --git a/.clang-format b/.clang-format
new file mode 100644
index 0000000..64f782a
--- /dev/null
+++ b/.clang-format
@@ -0,0 +1,62 @@
+---
+Language: Cpp
+BasedOnStyle: Google
+
+# Indentation
+IndentWidth: 4
+TabWidth: 4
+UseTab: Never
+AccessModifierOffset: -2
+NamespaceIndentation: None
+IndentCaseLabels: true
+
+# Line width
+ColumnLimit: 100
+
+# Braces
+BreakBeforeBraces: Attach
+AllowShortFunctionsOnASingleLine: Inline
+AllowShortIfStatementsOnASingleLine: Never
+AllowShortLoopsOnASingleLine: false
+AllowShortBlocksOnASingleLine: Empty
+
+# Includes
+SortIncludes: CaseSensitive
+IncludeBlocks: Regroup
+IncludeCategories:
+  # Project headers
+  - Regex:    '^"atp/'
+    Priority: 1
+  # System / C++ standard headers
+  - Regex:    '^<'
+    Priority: 2
+  # Catch-all
+  - Regex:    '.*'
+    Priority: 3
+
+# Alignment
+AlignAfterOpenBracket: Align
+AlignConsecutiveAssignments: false
+AlignConsecutiveDeclarations: false
+AlignOperands: Align
+AlignTrailingComments: true
+
+# Spacing
+SpaceAfterCStyleCast: false
+SpaceAfterTemplateKeyword: true
+SpaceBeforeAssignmentOperators: true
+SpaceBeforeParens: ControlStatements
+SpacesInAngles: Never
+
+# Pointer alignment
+PointerAlignment: Left
+ReferenceAlignment: Left
+DerivePointerAlignment: false
+
+# Other
+ReflowComments: true
+FixNamespaceComments: true
+CompactNamespaces: false
+AllowAllParametersOfDeclarationOnNextLine: true
+BinPackArguments: true
+BinPackParameters: true
diff --git a/.clang-tidy b/.clang-tidy
new file mode 100644
index 0000000..227c129
--- /dev/null
+++ b/.clang-tidy
@@ -0,0 +1,68 @@
+---
+# ATP Engine clang-tidy configuration
+#
+# Enable categories incrementally — start strict on the code we write,
+# avoid noise from auto-generated code (ANTLR4).
+
+Checks: >
+  -*,
+  bugprone-*,
+  -bugprone-easily-swappable-parameters,
+  clang-analyzer-*,
+  cppcoreguidelines-*,
+  -cppcoreguidelines-avoid-magic-numbers,
+  -cppcoreguidelines-pro-type-reinterpret-cast,
+  -cppcoreguidelines-pro-bounds-pointer-arithmetic,
+  -cppcoreguidelines-owning-memory,
+  misc-*,
+  -misc-non-private-member-variables-in-classes,
+  modernize-*,
+  -modernize-use-trailing-return-type,
+  performance-*,
+  readability-*,
+  -readability-magic-numbers,
+  -readability-identifier-length,
+
+WarningsAsErrors: ''
+
+HeaderFilterRegex: 'include/atp/.*\.h$'
+
+CheckOptions:
+  - key: readability-identifier-naming.NamespaceCase
+    value: lower_case
+  - key: readability-identifier-naming.ClassCase
+    value: CamelCase
+  - key: readability-identifier-naming.StructCase
+    value: CamelCase
+  - key: readability-identifier-naming.FunctionCase
+    value: camelBack
+  - key: readability-identifier-naming.VariableCase
+    value: lower_case
+  - key: readability-identifier-naming.MemberCase
+    value: lower_case
+  - key: readability-identifier-naming.MemberSuffix
+    value: '_'
+  - key: readability-identifier-naming.ConstantCase
+    value: CamelCase
+  - key: readability-identifier-naming.ConstantPrefix
+    value: k
+  - key: readability-identifier-naming.EnumConstantCase
+    value: CamelCase
+  - key: readability-identifier-naming.EnumConstantPrefix
+    value: k
+  - key: readability-identifier-naming.ConstexprVariableCase
+    value: CamelCase
+  - key: readability-identifier-naming.ConstexprVariablePrefix
+    value: k
+  - key: readability-identifier-naming.GlobalConstantCase
+    value: CamelCase
+  - key: readability-identifier-naming.GlobalConstantPrefix
+    value: k
+  - key: readability-identifier-naming.TemplateParameterCase
+    value: CamelCase
+  - key: performance-move-const-arg.CheckTriviallyCopyableMove
+    value: false
+  - key: cppcoreguidelines-special-member-functions.AllowSoleDefaultDtor
+    value: true
+  - key: readability-function-cognitive-complexity.Threshold
+    value: 25
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..7242ee6
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,14 @@
+# Build
+build/
+cmake-build-*/
+compile_commands.json
+
+# IDE
+.vscode/
+.idea/
+*.swp
+*~
+
+# OS
+.DS_Store
+Thumbs.db
diff --git a/CMakeLists.txt b/CMakeLists.txt
new file mode 100644
index 0000000..2cf69db
--- /dev/null
+++ b/CMakeLists.txt
@@ -0,0 +1,102 @@
+cmake_minimum_required(VERSION 3.20)
+project(atp_engine
+    VERSION   0.1.0
+    LANGUAGES CXX
+)
+
+# ─── C++ Standard ────────────────────────────────────────────────────────────
+set(CMAKE_CXX_STANDARD 20)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+set(CMAKE_CXX_EXTENSIONS OFF)
+
+# Export compile_commands.json for clang-tidy and IDE support
+set(CMAKE_EXPORT_COMPILE_COMMANDS ON)
+
+# ─── Compiler Warnings ──────────────────────────────────────────────────────
+add_compile_options(
+    -Wall -Wextra -Wpedantic
+    -Wshadow -Wnon-virtual-dtor
+    -Wold-style-cast -Wcast-align -Wunused
+    -Woverloaded-virtual -Wconversion -Wsign-conversion
+    -Wnull-dereference -Wdouble-promotion
+    -Wformat=2 -Wimplicit-fallthrough
+)
+
+# ─── Sanitizers (Debug builds) ───────────────────────────────────────────────
+option(ATP_ENABLE_SANITIZERS "Enable ASan + UBSan in Debug builds" ON)
+if(ATP_ENABLE_SANITIZERS AND CMAKE_BUILD_TYPE STREQUAL "Debug")
+    add_compile_options(-fsanitize=address,undefined -fno-omit-frame-pointer)
+    add_link_options(-fsanitize=address,undefined)
+endif()
+
+# ─── clang-tidy Integration ─────────────────────────────────────────────────
+option(ATP_ENABLE_CLANG_TIDY "Enable clang-tidy static analysis" OFF)
+if(ATP_ENABLE_CLANG_TIDY)
+    find_program(CLANG_TIDY_EXE NAMES clang-tidy)
+    if(CLANG_TIDY_EXE)
+        set(CMAKE_CXX_CLANG_TIDY "${CLANG_TIDY_EXE}")
+        message(STATUS "clang-tidy found: ${CLANG_TIDY_EXE}")
+    else()
+        message(WARNING "clang-tidy requested but not found")
+    endif()
+endif()
+
+# ─── clang-format Custom Target ─────────────────────────────────────────────
+find_program(CLANG_FORMAT_EXE NAMES clang-format)
+if(CLANG_FORMAT_EXE)
+    file(GLOB_RECURSE ALL_CXX_SOURCES
+        ${PROJECT_SOURCE_DIR}/src/*.cc
+        ${PROJECT_SOURCE_DIR}/include/*.h
+        ${PROJECT_SOURCE_DIR}/tests/*.cc
+    )
+    add_custom_target(format
+        COMMAND ${CLANG_FORMAT_EXE} -i ${ALL_CXX_SOURCES}
+        COMMENT "Running clang-format on all source files"
+        VERBATIM
+    )
+    add_custom_target(format-check
+        COMMAND ${CLANG_FORMAT_EXE} --dry-run --Werror ${ALL_CXX_SOURCES}
+        COMMENT "Checking clang-format compliance"
+        VERBATIM
+    )
+    message(STATUS "clang-format found: ${CLANG_FORMAT_EXE}")
+    message(STATUS "  Use 'cmake --build . --target format'       to auto-format")
+    message(STATUS "  Use 'cmake --build . --target format-check' to check format")
+else()
+    message(WARNING "clang-format not found, format targets disabled")
+endif()
+
+# ─── Source Files ────────────────────────────────────────────────────────────
+set(ATP_SOURCES
+    src/core/symbol_table.cc
+    src/core/term_bank.cc
+    src/core/clause_store.cc
+    src/normalize/clausifier.cc
+    src/infer/unification.cc
+    src/infer/resolution.cc
+    src/index/discrim_tree.cc
+    src/simplify/subsumption.cc
+    src/search/prover.cc
+    src/proof/proof_trace.cc
+    src/rewrite/ordering.cc
+    src/rewrite/paramodulation.cc
+    src/strategy/problem_analyzer.cc
+    src/frontend/tptp_parser.cc
+)
+
+# ─── Core Library ────────────────────────────────────────────────────────────
+add_library(atp_core STATIC ${ATP_SOURCES})
+target_include_directories(atp_core PUBLIC
+    ${PROJECT_SOURCE_DIR}/include
+)
+
+# ─── Main Executable ────────────────────────────────────────────────────────
+add_executable(atp src/main.cc)
+target_link_libraries(atp PRIVATE atp_core)
+
+# ─── Tests ───────────────────────────────────────────────────────────────────
+option(ATP_BUILD_TESTS "Build unit tests" ON)
+if(ATP_BUILD_TESTS)
+    enable_testing()
+    add_subdirectory(tests)
+endif()
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..f288702
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,674 @@
+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
+
+  The GNU General Public License is a free, copyleft license for
+software and other kinds of works.
+
+  The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works.  By contrast,
+the GNU General Public License is intended to guarantee your freedom to
+share and change all versions of a program--to make sure it remains free
+software for all its users.  We, the Free Software Foundation, use the
+GNU General Public License for most of our software; it applies also to
+any other work released this way by its authors.  You can apply it to
+your programs, too.
+
+  When we speak of free software, we are referring to freedom, not
+price.  Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+them if you wish), that you receive source code or can get it if you
+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+  To protect your rights, we need to prevent others from denying you
+these rights or asking you to surrender the rights.  Therefore, you have
+certain responsibilities if you distribute copies of the software, or if
+you modify it: responsibilities to respect the freedom of others.
+
+  For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must pass on to the recipients the same
+freedoms that you received.  You must make sure that they, too, receive
+or can get the source code.  And you must show them these terms so they
+know their rights.
+
+  Developers that use the GNU GPL protect your rights with two steps:
+(1) assert copyright on the software, and (2) offer you this License
+giving you legal permission to copy, distribute and/or modify it.
+
+  For the developers' and authors' protection, the GPL clearly explains
+that there is no warranty for this free software.  For both users' and
+authors' sake, the GPL requires that modified versions be marked as
+changed, so that their problems will not be attributed erroneously to
+authors of previous versions.
+
+  Some devices are designed to deny users access to install or run
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+  Finally, every program is threatened constantly by software patents.
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+  The precise terms and conditions for copying, distribution and
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+
+                       TERMS AND CONDITIONS
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+  "This License" refers to version 3 of the GNU General Public License.
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diff --git a/README.md b/README.md
new file mode 100644
index 0000000..ac0ccd6
--- /dev/null
+++ b/README.md
@@ -0,0 +1,49 @@
+# ATP Engine
+
+A saturation-based automated theorem prover for first-order logic, written in C++20.
+
+## Overview
+
+ATP Engine implements the **Given Clause Loop** (Otter/E-style) with hash-consed term sharing, discrimination tree indexing, and pluggable search heuristics. It reads problems in [TPTP](https://www.tptp.org/) format and produces human-readable proofs via resolution and factoring.
+
+The architecture is designed for extensibility toward equality reasoning (superposition), sorted logic, and theory integration. See [`docs/architecture.md`](docs/architecture.md) for full design documentation.
+
+## Build
+
+Requires CMake 3.20+ and a C++20 compiler (GCC 11+ / Clang 14+).
+
+```bash
+cmake -B build -DCMAKE_BUILD_TYPE=Debug
+cmake --build build -j$(nproc)
+```
+
+### Options
+
+| Flag | Default | Description |
+|------|---------|-------------|
+| `ATP_ENABLE_CLANG_TIDY` | `OFF` | Run clang-tidy during compilation |
+| `ATP_ENABLE_SANITIZERS` | `ON` | ASan + UBSan in Debug builds |
+| `ATP_BUILD_TESTS` | `ON` | Build GoogleTest unit tests |
+
+### Format & Lint
+
+```bash
+cmake --build build --target format        # auto-format all sources
+cmake --build build --target format-check  # check format compliance
+```
+
+## Run
+
+```bash
+./build/atp data/monkey_banana.p
+```
+
+## Test
+
+```bash
+cd build && ctest --output-on-failure
+```
+
+## License
+
+This project is licensed under the [GNU General Public License v3.0](https://www.gnu.org/licenses/gpl-3.0.html). Also see [LICENSE](LICENSE)
diff --git a/data/monkey_banana.p b/data/monkey_banana.p
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/data/monkey_banana.p
diff --git a/docs/architecture.md b/docs/architecture.md
new file mode 100644
index 0000000..333fa99
--- /dev/null
+++ b/docs/architecture.md
@@ -0,0 +1,630 @@
+# ATP Engine — Architecture Design Document
+
+> **Version**: 1.0  
+> **Target**: Extensible first-order logic theorem prover (saturation-based)  
+> **Language**: C++20  
+> **Build**: CMake 3.20+, GoogleTest, ANTLR4 (C++ target)
+
+---
+
+## Table of Contents
+
+1. [Design Philosophy](#1-design-philosophy)
+2. [System Architecture](#2-system-architecture)
+3. [Directory Structure](#3-directory-structure)
+4. [Module Specifications](#4-module-specifications)
+5. [Data Flow](#5-data-flow)
+6. [Known Limitations & Future Work](#6-known-limitations--future-work)
+7. [References](#7-references)
+
+---
+
+## 1. Design Philosophy
+
+### 1.1 Core Principles
+
+| Principle | Rationale |
+|-----------|-----------|
+| **Bottom-up construction** | Build from the memory layer upward. A stable Term Bank is the foundation everything else rests on. |
+| **Strict layered dependencies** | Dependencies flow in one direction only: `core → infer → index → simplify → search → proof`. No cycles. |
+| **Interface-implementation separation** | Headers in `include/atp/` define interfaces; `src/` contains implementations. Modules communicate through stable APIs. |
+| **Premature abstraction avoidance** | V1 hardcodes resolution + factoring. Abstract strategy selection (`strategy/`) is scaffolded but not wired in until V2. |
+| **Parse once, reason forever** | Text parsing (ANTLR4) is a one-shot frontend concern. The core engine operates entirely on integer IDs, never on strings. |
+
+### 1.2 Design Influences
+
+This architecture draws from three production-grade theorem provers:
+
+- **E Prover** (Stephan Schulz) — Given Clause Loop, term sharing via hash consing, age-weight clause selection.
+- **Vampire** (Andrei Voronkov et al.) — AVATAR splitting, superposition calculus, discrimination tree indexing.
+- **Otter** (William McCune) — Original set-of-support strategy, subsumption, demodulation.
+
+### 1.3 Versioning Strategy
+
+```
+V1  →  Pure first-order resolution (no equality). Solve the Monkey-Banana problem.
+V2  →  Pluggable inference rules (Calculus), age-weight scheduling, variable standardization.
+V3  →  Equality reasoning (paramodulation/superposition), term orderings (KBO/LPO).
+V4  →  AVATAR splitting, SAT solver integration, TPTP competition readiness.
+```
+
+---
+
+## 2. System Architecture
+
+### 2.1 Layered Architecture Overview
+
+```
+┌──────────────────────────────────────────────────────────────────────┐
+│                         Frontend Layer                               │
+│  TPTP File → ANTLR4 Lexer/Parser → AST Builder → tptp_parser.h     │
+└────────────────────────────────┬─────────────────────────────────────┘
+                                 │ Formula (internal AST)
+┌────────────────────────────────▼─────────────────────────────────────┐
+│                       Normalization Layer                             │
+│  formula.h → clausifier.h (NNF → Skolem → CNF)                     │
+└────────────────────────────────┬─────────────────────────────────────┘
+                                 │ Clause set
+┌────────────────────────────────▼─────────────────────────────────────┐
+│                        Search Layer (Control)                        │
+│                                                                      │
+│   ┌──────────────┐  select   ┌─────────────────┐  resolve with all  │
+│   │ Unprocessed  │─────────→ │  Given Clause   │─────────────────→  │
+│   │ (pri queue)  │           │  (selected)     │                    │
+│   └──────▲───────┘           └─────────────────┘                    │
+│          │ enqueue survivors                                         │
+│   ┌──────┴───────┐           ┌─────────────────┐                    │
+│   │  Simplify &  │←──────────│  New Clauses    │                    │
+│   │  Filter      │           │  (resolvents)   │                    │
+│   └──────────────┘           └─────────────────┘                    │
+│          │ if empty clause found                                     │
+└──────────┼───────────────────────────────────────────────────────────┘
+           ▼
+┌──────────────────────────────────────────────────────────────────────┐
+│                         Output Layer                                 │
+│  proof_trace.h → DFS backtrack → format & print action sequence     │
+└──────────────────────────────────────────────────────────────────────┘
+
+═══════════════════════ Shared Foundation ══════════════════════════════
+┌──────────────────────────────────────────────────────────────────────┐
+│                    Core Layer (Data Plane)                            │
+│  Symbol Table │ Term Bank (hash consing) │ Clause Store │ Types     │
+└──────────────────────────────────────────────────────────────────────┘
+```
+
+### 2.2 Dependency Graph
+
+```
+frontend ──→ normalize ──→ core
+                             ↑
+search ──→ simplify ──→ index ──→ infer ──→ core
+                                             ↑
+                                         rewrite ─┘
+  proof ──→ core/clause_store
+
+  strategy/ ──→ (V2: wired into search)
+```
+
+All arrows point downward/inward. `proof` depends only on `clause_store`, not on `search` (no reverse dependency).
+
+---
+
+## 3. Directory Structure
+
+```
+richard-atp-engine/
+├── CMakeLists.txt                # Top-level build (C++20, clang-tidy, clang-format, sanitizers)
+├── .clang-format                 # Google-based, 4-space indent, 100-col
+├── .clang-tidy                   # Strict checks, filtered for generated code
+├── .gitignore
+│
+├── grammar/
+│   └── TPTP.g4                   # ANTLR4 grammar for TPTP fof/cnf syntax
+│
+├── docs/
+│   └── architecture.md           # This document
+│
+├── data/
+│   └── monkey_banana.p           # First integration test (TPTP format)
+│
+├── include/atp/
+│   ├── core/                     # Data plane — memory foundation
+│   │   ├── types.h               #   TermId, ClauseId, SymbolId, SortId, SymbolKind, InferenceRule
+│   │   ├── symbol_table.h        #   String interning with kind/sort metadata
+│   │   ├── term.h                #   Flat term struct (symbol_id + args)
+│   │   ├── literal.h             #   Polarity + atom TermId
+│   │   ├── clause.h              #   Literal vector + provenance (parents, rule, depth)
+│   │   ├── clause_store.h        #   Central clause ownership, ClauseId allocation
+│   │   └── term_bank.h           #   Hash-consing pool for structural sharing
+│   │
+│   ├── normalize/                # Normalization — FOL formula to CNF
+│   │   ├── formula.h             #   FOL AST nodes (And, Or, Not, Forall, Exists, ...)
+│   │   └── clausifier.h          #   Eliminate →/↔ → NNF → Skolemize → distribute → flatten
+│   │
+│   ├── infer/                    # Compute plane — stateless inference operators
+│   │   ├── substitution.h        #   Variable binding map (stack-lifetime)
+│   │   ├── unification.h         #   MGU with optional occurs check
+│   │   └── resolution.h          #   Binary resolution + factoring
+│   │
+│   ├── index/                    # Index plane — fast term retrieval
+│   │   └── discrim_tree.h        #   Discrimination tree (unifiable / instance / generalization queries)
+│   │
+│   ├── simplify/                 # Redundancy elimination
+│   │   ├── tautology.h           #   Complementary literal detection
+│   │   └── subsumption.h         #   Forward/backward subsumption (backed by discrim tree)
+│   │
+│   ├── search/                   # Control plane — proof search scheduling
+│   │   ├── clause_queue.h        #   Comparators (BFS, weight-based)
+│   │   └── prover.h              #   Given Clause Loop (V1: hardcoded rules; V2: Calculus-driven)
+│   │
+│   ├── proof/                    # Output — proof reconstruction
+│   │   └── proof_trace.h         #   DFS backtrack from empty clause, formatting
+│   │
+│   ├── rewrite/                  # Equality reasoning (V3 extension point)
+│   │   ├── ordering.h            #   Abstract TermOrdering (KBO, LPO)
+│   │   └── paramodulation.h      #   Paramodulation + demodulation
+│   │
+│   ├── strategy/                 # Dynamic algorithm selection (V2 extension point)
+│   │   ├── inference_rule.h      #   GeneratingRule / SimplifyingRule interfaces
+│   │   ├── calculus.h            #   Bundles rules + heuristics + ordering
+│   │   └── problem_analyzer.h   #   Feature detection + calculus selection
+│   │
+│   └── utils/
+│       ├── hash_utils.h          #   Hash combination (boost::hash_combine equivalent)
+│       └── logger.h              #   Compile-time-filtered logging macros
+│
+├── src/                          # Implementation files (mirror include/ structure)
+│   ├── core/
+│   ├── normalize/
+│   ├── infer/
+│   ├── index/
+│   ├── simplify/
+│   ├── search/
+│   ├── proof/
+│   ├── rewrite/
+│   ├── strategy/
+│   ├── frontend/
+│   └── main.cpp
+│
+└── tests/                        # GoogleTest unit tests
+    ├── CMakeLists.txt
+    ├── test_term_bank.cc
+    ├── test_unification.cc
+    ├── test_clausifier.cc
+    ├── test_resolution.cc
+    ├── test_discrim_tree.cc
+    └── test_prover.cc           # End-to-end: Monkey-Banana problem
+```
+
+---
+
+## 4. Module Specifications
+
+### 4.1 Core Layer (`core/`)
+
+The core layer owns all persistent data. Every other module receives `const&` or `&` references to core objects — never raw pointers, never ownership.
+
+#### `types.h` — Type System Foundation
+
+```cpp
+using SymbolId = uint32_t;   // Index into SymbolTable
+using TermId   = uint32_t;   // Index into TermBank (hash-consed)
+using ClauseId = uint32_t;   // Index into ClauseStore
+using SortId   = uint16_t;   // For sorted logic (V3+), default = kUnsorted
+
+enum class SymbolKind : uint8_t {
+    kVariable, kConstant, kFunction, kPredicate, kSkolem
+};
+
+enum class InferenceRule : uint16_t {
+    kInput = 0, kResolution = 1, kFactoring = 2,       // Core
+    kParamodulation = 100, kDemodulation = 101, ...     // Equality (V3)
+    kSubsumption = 200, kTautologyElim = 201, ...       // Simplification
+    kTheoryResolution = 300, ...                         // Theory (V4)
+};
+```
+
+**Design decisions**:
+- `uint32_t` IDs instead of pointers — enables flat array storage, trivial comparison, and cache-friendly iteration.
+- `InferenceRule` uses `uint16_t` with reserved ranges (0-99 core, 100-199 equality, 200-299 simplification, 300+ theory) to avoid enum churn as the system grows.
+- `SymbolKind` enables distinguishing variables from function symbols at the symbol level, critical for unification and sorted logic.
+- `SortId` is present but unused in V1 (`kUnsorted`), ready for sorted unification in V3.
+
+#### `symbol_table.h` — String Interning
+
+```cpp
+struct SymbolInfo {
+    std::string name;
+    SymbolKind kind;
+    uint16_t arity;
+    SortId sort;
+};
+
+class SymbolTable {
+    SymbolId intern(string_view name, SymbolKind kind, uint16_t arity, SortId sort);
+    string_view getName(SymbolId id) const;
+    const SymbolInfo& getInfo(SymbolId id) const;
+    bool isVariable(SymbolId id) const;
+};
+```
+
+Each unique symbol string is stored exactly once. All downstream modules work with `SymbolId` integers. The `SymbolInfo` metadata (kind, arity, sort) enables type-checking during unification without string inspection.
+
+#### `term_bank.h` — Hash Consing
+
+```cpp
+class TermBank {
+    TermId makeTerm(SymbolId symbol, span<const TermId> args);
+    TermId makeVar(SymbolId var_symbol);
+    const Term& getTerm(TermId id) const;
+    bool isVariable(TermId id) const;
+};
+```
+
+**Hash consing guarantee**: If `makeTerm(f, {a, b})` is called twice with the same `f`, `a`, `b`, it returns the same `TermId`. This makes structural equality a single integer comparison (`O(1)`), which is the foundation for efficient indexing and subsumption.
+
+**Memory layout**: Terms are stored in a flat arena. Each `Term` header (`symbol_id` + `arity`) is followed by its argument `TermId` array in contiguous memory. No heap allocation per term.
+
+#### `clause_store.h` — Clause Ownership
+
+```cpp
+class ClauseStore {
+    ClauseId addClause(Clause clause);
+    const Clause& getClause(ClauseId id) const;
+    Clause& getMutableClause(ClauseId id);
+    void forEach(const function<void(const Clause&)>& visitor) const;
+};
+```
+
+Separated from `Prover` so that proof extraction, simplification, and search all access clauses through the same stable interface. Changing the search strategy (OTTER loop → DISCOUNT loop) does not affect clause storage.
+
+---
+
+### 4.2 Normalization Layer (`normalize/`)
+
+#### `formula.h` — First-Order Logic AST
+
+```cpp
+enum class FormulaKind : uint8_t {
+    kAtom, kNot, kAnd, kOr, kImplies, kIff, kForall, kExists
+};
+
+struct Formula {
+    FormulaKind kind;
+    TermId atom;                              // for kAtom
+    string var_name;                          // for quantifiers
+    vector<unique_ptr<Formula>> children;     // sub-formulas
+};
+```
+
+This is the **pre-clausification** representation. The parser builds `Formula` trees; the clausifier destroys them and produces `Clause` vectors. Formula nodes are short-lived — they exist only during the normalization phase.
+
+#### `clausifier.h` — CNF Conversion Pipeline
+
+```
+Input Formula
+    │
+    ▼ eliminateImplication()     — P → Q  becomes  ¬P ∨ Q
+    ▼ eliminateBiconditional()   — P ↔ Q  becomes  (¬P ∨ Q) ∧ (P ∨ ¬Q)
+    ▼ pushNegation()             — ¬(P ∧ Q) becomes ¬P ∨ ¬Q       (NNF)
+    ▼ skolemize()                — ∀x∃y.P(x,y) becomes ∀x.P(x, sk(x))
+    ▼ dropUniversal()            — All remaining vars are implicitly ∀
+    ▼ distribute()               — (P ∨ (Q ∧ R)) becomes (P ∨ Q) ∧ (P ∨ R)
+    ▼ flatten()                  — Nested ∧ at top level → separate clauses
+    │
+    ▼
+Output: vector<Clause>
+```
+
+**Critical**: `skolemize()` must correctly handle nested quantifier scopes. Given `∀x ∃y ∀z ∃w. P(x,y,z,w)`, the Skolem functions are `y = sk1(x)` and `w = sk2(x, z)` — each existential variable becomes a function of all universally quantified variables in its scope.
+
+---
+
+### 4.3 Inference Layer (`infer/`)
+
+#### `substitution.h` — Variable Bindings
+
+A substitution `σ = {X → f(a), Y → Z}` maps variables to terms. Key properties:
+
+- **Stack lifetime**: Created during unification, applied to build the resolvent, then discarded. Never stored long-term.
+- **Chain resolution**: `resolve(X)` walks the binding chain (`X → Y → f(a)`) to the final value.
+- **Idempotence**: After applying a substitution, no variables in the result have bindings in the same substitution.
+
+#### `unification.h` — Most General Unifier
+
+```cpp
+bool unify(const TermBank& bank, TermId t1, TermId t2, Substitution& subst,
+           const UnificationConfig& config);
+```
+
+The Robinson unification algorithm, operating on `TermId` values via the `TermBank`. Returns the Most General Unifier (MGU) if one exists.
+
+**Occurs check**: Configurable via `UnificationConfig::enable_occurs_check`. Disabled for situation calculus planning (performance); enabled for general mathematical reasoning (soundness — prevents infinite terms like `X = f(X)`).
+
+#### `resolution.h` — Inference Rules
+
+```cpp
+optional<Clause> resolve(bank, clause1, lit_idx1, clause2, lit_idx2);
+vector<Clause>   allResolvents(bank, clause1, clause2);
+vector<Clause>   factor(bank, clause);
+```
+
+**Binary resolution**: Given clauses `{P(x), Q(x)}` and `{¬P(a), R(a)}`, if `P(x)` and `P(a)` unify under `σ = {x→a}`, produce resolvent `{Q(a), R(a)}`.
+
+**Factoring**: Given clause `{P(x), P(a), Q(x)}`, if `P(x)` and `P(a)` unify, produce `{P(a), Q(a)}`. Factoring is necessary for completeness of binary resolution.
+
+---
+
+### 4.4 Index Layer (`index/`)
+
+#### `discrim_tree.h` — Discrimination Tree
+
+A trie-based index over the flattened structure of terms. Supports three query types:
+
+| Query | Use Case | Direction |
+|-------|----------|-----------|
+| `queryUnifiable(t)` | Find resolution partners | Bidirectional matching |
+| `queryInstances(t)` | Backward subsumption | Pattern more general than indexed |
+| `queryGeneralizations(t)` | Forward subsumption | Indexed more general than query |
+
+The tree is built by linearizing terms in pre-order: `f(g(a), b)` becomes the key sequence `[f, g, a, *, b]` where `*` represents a variable (wildcard). Lookups traverse the trie, branching at decision points.
+
+---
+
+### 4.5 Simplification Layer (`simplify/`)
+
+#### `tautology.h`
+
+Detects clauses containing both `P` and `¬P` for the same atom. These are logically true and can be safely discarded without affecting completeness.
+
+#### `subsumption.h`
+
+Backed by the discrimination tree. Two operations:
+
+- **Forward subsumption**: Before enqueuing a new clause `C`, check if any existing clause `D` subsumes it (`D ⊆ C` — every literal of `D` matches a literal of `C`). If yes, discard `C`.
+- **Backward subsumption**: After adding `C`, check if `C` subsumes any existing clause `D`. If yes, remove `D`.
+
+Subsumption is the single most important simplification rule for keeping the clause set manageable.
+
+---
+
+### 4.6 Search Layer (`search/`)
+
+#### `prover.h` — The Given Clause Loop
+
+The main proof search loop, following the OTTER/E paradigm:
+
+```
+procedure GivenClauseLoop(initial_clauses):
+    Unprocessed ← priority_queue(initial_clauses)
+    Processed   ← empty_set
+
+    while Unprocessed is not empty:
+        given ← Unprocessed.pop()          // clause selection
+
+        if given is tautology: continue
+        if given is forward-subsumed: continue
+
+        // Backward simplification
+        remove from Processed all clauses subsumed by given
+
+        // Inference
+        for each clause C in Processed:
+            for each resolvent R of (given, C):
+                if R is empty clause: RETURN PROOF FOUND
+                if R is not tautology and not forward-subsumed:
+                    Unprocessed.push(R)
+
+        // Generate factors of given
+        for each factor F of given:
+            if F is empty clause: RETURN PROOF FOUND
+            Unprocessed.push(F)
+
+        Processed.add(given)
+
+    RETURN SATURATED (no proof exists)
+```
+
+**V1 configuration**:
+```cpp
+struct ProverConfig {
+    ClauseComparator comparator = bfsCompare;  // BFS for shortest proof
+    size_t max_clauses = 100000;
+    size_t max_iterations = 500000;
+    bool enable_occurs_check = false;
+};
+```
+
+---
+
+### 4.7 Proof Layer (`proof/`)
+
+#### `proof_trace.h`
+
+When the empty clause `□` is derived, the prover halts. Proof extraction walks the `parent1`/`parent2` pointers stored in each `Clause` via DFS, reconstructing the derivation tree from `□` back to input axioms.
+
+The output is a sequence of `ProofStep` records, each containing the inference rule used and the parent clause IDs. This can be formatted as a human-readable proof or (future) TSTP-compliant output.
+
+---
+
+### 4.8 Extension Point: Rewriting (`rewrite/`)
+
+Scaffolded for V3. Not compiled in V1.
+
+#### `ordering.h` — Abstract Term Ordering
+
+```cpp
+class TermOrdering {
+    virtual OrderResult compare(const TermBank& bank, TermId t1, TermId t2) const = 0;
+};
+```
+
+Concrete implementations (future): Knuth-Bendix Ordering (KBO), Lexicographic Path Ordering (LPO). These are required for ordered resolution and superposition calculus — they ensure that rewriting always terminates.
+
+#### `paramodulation.h` — Equality Reasoning
+
+Paramodulation replaces a subterm in one clause with an equal term from another. Combined with a term ordering, this becomes the **superposition calculus** — the dominant approach for first-order logic with equality.
+
+---
+
+### 4.9 Extension Point: Strategy (`strategy/`)
+
+Scaffolded for V2. Not compiled in V1.
+
+The strategy module will enable dynamic algorithm selection based on problem analysis:
+
+```
+Input clauses → ProblemAnalyzer → ProblemFeatures → selectCalculus() → Calculus
+                                                                         │
+                        ┌────────────────────────────────────────────────┘
+                        ▼
+             Calculus = { generating_rules[], simplifying_rules[],
+                          comparator, ordering, resource_limits }
+                        │
+                        ▼
+                   Prover.prove(calculus)
+```
+
+This prevents search space explosion by loading only the inference rules relevant to the problem. A pure propositional problem would never load the paramodulation rule; an equality-heavy problem would skip pure resolution in favor of superposition.
+
+---
+
+## 5. Data Flow
+
+### 5.1 End-to-End Pipeline
+
+```
+monkey_banana.p (TPTP text file)
+       │
+       ▼
+  [tptp_parser]  ANTLR4 lexer/parser → parse tree → Formula AST
+       │
+       ▼
+  [clausifier]   NNF → Skolemize → CNF → vector<Clause>
+       │
+       ▼
+  [prover]       Given Clause Loop (resolution + factoring + subsumption)
+       │
+       ├── Normal: derive new clauses, enqueue, repeat
+       │
+       └── Empty clause found!
+              │
+              ▼
+        [proof_trace]  DFS backtrack through parent pointers
+              │
+              ▼
+        Human-readable proof output
+```
+
+### 5.2 Term Lifecycle
+
+```
+String "do(walk, S0)"
+       │
+       ▼ SymbolTable::intern()
+  SymbolIds: { do=0, walk=1, S0=2 }
+       │
+       ▼ TermBank::makeTerm()
+  TermIds:   S0_term=0, walk_term=1, do_walk_S0=2
+       │     (hash-consed: calling makeTerm(do, [walk, S0]) again returns 2)
+       │
+       ▼ Used everywhere as integer IDs
+  Clause { literals: [ Literal{atom=2, positive=true} ] }
+```
+
+### 5.3 Substitution Lifecycle
+
+```
+Unify( P(X, f(Y)),  P(a, f(b)) )
+       │
+       ▼ unify() creates stack-local Substitution
+  σ = { X → a,  Y → b }
+       │
+       ▼ Apply σ to build resolvent clause
+  New terms created in TermBank (hash-consed)
+       │
+       ▼ Substitution goes out of scope — destroyed
+  Only the new TermIds persist
+```
+
+---
+
+## 6. Known Limitations & Future Work
+
+### 6.1 Critical Gaps (Ordered by Priority)
+
+#### Gap 1: No Variable Standardization Apart
+
+**Impact**: Correctness bug if not addressed before first real resolution.
+
+When resolving clause `{P(X)}` with clause `{¬P(X), Q(X)}`, variable `X` in the two clauses must be treated as distinct. Without renaming one clause's variables (e.g., `X → X'`), the unifier incorrectly constrains both clauses' variables.
+
+**Fix**: Add `renameVariables(Clause&, TermBank&, uint32_t& next_var_id)` to `infer/` before Phase 2 resolution implementation.
+
+#### Gap 2: No Literal Selection Function
+
+**Impact**: Search space is ~10x larger than necessary.
+
+Ordered resolution restricts inference to the **maximal literal** (under a term ordering) in each clause. Our `Prover` currently has no concept of selecting which literal to resolve on — it tries all pairs.
+
+**Fix**: V2 — add `LiteralSelector` interface, parameterized by `TermOrdering`.
+
+#### Gap 3: Single Clause Queue (No Age-Weight Interleaving)
+
+**Impact**: Incomplete or extremely slow on hard problems.
+
+A single `ClauseComparator` cannot implement the age-weight ratio that E Prover uses: "pick the lightest clause 5 times, then the oldest clause once." This interleaving is crucial for both performance and completeness.
+
+**Fix**: V2 — replace `ClauseComparator` with a `ClauseQueue` abstract class supporting multi-queue round-robin.
+
+#### Gap 4: Single Index Type
+
+**Impact**: Suboptimal retrieval performance.
+
+The discrimination tree handles forward matching well but is not ideal for all query patterns. Modern ATPs maintain multiple complementary indices:
+
+| Index Type | Best For |
+|-----------|----------|
+| Discrimination Tree | Forward matching (generalization queries) |
+| Substitution Tree | Backward matching + unification candidates |
+| Fingerprint Index | O(1) pre-filtering of non-unifiable pairs |
+| Feature Vector Index | Clause-level subsumption checks |
+
+**Fix**: V3 — abstract `TermIndex` interface, multiple implementations.
+
+#### Gap 5: No Preprocessing Pipeline
+
+**Impact**: Missed optimization opportunities.
+
+Between clausification and the main loop, modern ATPs perform definition unfolding, pure literal elimination, equality axiom injection, and miniscoping. Our `normalize/` layer has only the clausifier.
+
+**Fix**: V2 — extend `normalize/` into a transform pipeline with pluggable passes.
+
+#### Gap 6: No AVATAR Splitting
+
+**Impact**: Cannot compete on structured problems.
+
+AVATAR splits clauses with independent variable sets into propositional components managed by an embedded SAT solver. This is the single largest performance innovation in ATP in the last decade (10-100x speedup on structured problems).
+
+**Fix**: V4 — add `sat/` module with MiniSat/CaDiCaL integration + splitting logic in `search/`.
+
+### 6.2 Non-Critical Gaps
+
+| Gap | Category | Target Version |
+|-----|----------|----------------|
+| TSTP proof output format | Interoperability | V2 |
+| Watched literals for unit propagation | Performance | V3 |
+| Clause arena (replace `vector<Literal>`) | Memory | V3 |
+| ML-guided clause selection | Research | V5+ |
+| Parallel portfolio mode | Performance | V5+ |
+
+---
+
+## 7. References
+
+1. Schulz, S. (2013). *System Description: E 1.8*. CADE-24.
+2. Kovács, L., Voronkov, A. (2013). *First-Order Theorem Proving and Vampire*. CAV 2013.
+3. Voronkov, A. (2014). *AVATAR: The Architecture for First-Order Theorem Provers*. CAV 2014.
+4. Nieuwenhuis, R., Rubio, A. (2001). *Paramodulation-Based Theorem Proving*. Handbook of Automated Reasoning.
+5. Sutcliffe, G. (2009). *The TPTP Problem Library and Associated Infrastructure*. Journal of Automated Reasoning.
+6. Robinson, J.A. (1965). *A Machine-Oriented Logic Based on the Resolution Principle*. JACM.
diff --git a/grammar/TPTP.g4 b/grammar/TPTP.g4
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/grammar/TPTP.g4
diff --git a/include/atp/core/clause.h b/include/atp/core/clause.h
new file mode 100644
index 0000000..b4d3e68
--- /dev/null
+++ b/include/atp/core/clause.h
@@ -0,0 +1,53 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file clause.h
+/// @brief A clause is a disjunction of literals, with provenance tracking.
+///
+/// NOTE: V1 uses std::vector<Literal> for simplicity.
+/// Future optimization: migrate to a Clause Arena with contiguous storage.
+
+#include <vector>
+
+#include "atp/core/literal.h"
+#include "atp/core/types.h"
+
+namespace atp {
+
+/// A clause: a disjunction of literals plus provenance for proof reconstruction.
+struct Clause {
+    ClauseId id = kInvalidId;
+    std::vector<Literal> literals;
+
+    // Provenance (for proof trace)
+    InferenceRule rule = InferenceRule::kInput;
+    ClauseId parent1 = kInvalidId;
+    ClauseId parent2 = kInvalidId;
+    uint16_t depth = 0;  ///< Derivation depth (for BFS scheduling)
+
+    /// True if the clause has no literals (contradiction).
+    [[nodiscard]] bool isEmpty() const { return literals.empty(); }
+
+    /// Number of literals.
+    [[nodiscard]] size_t size() const { return literals.size(); }
+};
+
+}  // namespace atp
diff --git a/include/atp/core/clause_store.h b/include/atp/core/clause_store.h
new file mode 100644
index 0000000..6e220cc
--- /dev/null
+++ b/include/atp/core/clause_store.h
@@ -0,0 +1,62 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file clause_store.h
+/// @brief Central clause storage — owns all clauses, assigns ClauseIds.
+///
+/// Extracted from Prover to separate storage responsibility from search logic.
+/// This enables swapping search strategies (OTTER loop / DISCOUNT loop)
+/// without touching clause lifecycle management.
+
+#include "atp/core/clause.h"
+#include "atp/core/types.h"
+
+#include <functional>
+#include <vector>
+
+namespace atp {
+
+/// Central clause store. Owns all clauses and assigns unique ClauseIds.
+/// All modules access clauses through this store via ClauseId references.
+class ClauseStore {
+  public:
+    ClauseStore() = default;
+
+    /// Add a clause, assign it a ClauseId, and return the ID.
+    ClauseId addClause(Clause clause);
+
+    /// Access a clause by its ID. UB if id is out of range.
+    [[nodiscard]] const Clause& getClause(ClauseId id) const;
+
+    /// Mutable access (for marking clauses as deleted, etc.)
+    [[nodiscard]] Clause& getMutableClause(ClauseId id);
+
+    /// Total number of stored clauses.
+    [[nodiscard]] size_t size() const;
+
+    /// Iterate over all clauses with a visitor.
+    void forEach(const std::function<void(const Clause&)>& visitor) const;
+
+  private:
+    std::vector<Clause> clauses_;
+};
+
+}  // namespace atp
diff --git a/include/atp/core/literal.h b/include/atp/core/literal.h
new file mode 100644
index 0000000..1b4f65c
--- /dev/null
+++ b/include/atp/core/literal.h
@@ -0,0 +1,40 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file literal.h
+/// @brief A literal is a (possibly negated) atomic formula.
+
+#include "atp/core/types.h"
+
+namespace atp {
+
+/// A literal: a polarity flag plus the TermId of the atom.
+struct Literal {
+    TermId atom;         ///< TermId of the predicate application
+    bool is_positive;    ///< true = positive, false = negated
+
+    /// Complement: flip polarity, same atom.
+    [[nodiscard]] Literal complement() const { return {atom, !is_positive}; }
+
+    bool operator==(const Literal& other) const = default;
+};
+
+}  // namespace atp
diff --git a/include/atp/core/symbol_table.h b/include/atp/core/symbol_table.h
new file mode 100644
index 0000000..ed27a4d
--- /dev/null
+++ b/include/atp/core/symbol_table.h
@@ -0,0 +1,68 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file symbol_table.h
+/// @brief Bidirectional mapping between symbol names and SymbolIds,
+///        with kind and sort metadata.
+
+#include <string>
+#include <string_view>
+
+#include "atp/core/types.h"
+
+namespace atp {
+
+/// Metadata associated with an interned symbol.
+struct SymbolInfo {
+    std::string name;
+    SymbolKind kind = SymbolKind::kFunction;
+    uint16_t arity = 0;
+    SortId sort = kUnsorted;  ///< Result sort (for sorted logic)
+};
+
+/// Interns symbol names so that each unique string is stored exactly once.
+/// Also tracks symbol metadata (kind, arity, sort).
+/// Thread-safety: NOT thread-safe (single-threaded prover design).
+class SymbolTable {
+  public:
+    SymbolTable() = default;
+
+    /// Intern a symbol name with metadata. Returns existing ID if already present.
+    SymbolId intern(std::string_view name, SymbolKind kind, uint16_t arity = 0,
+                    SortId sort = kUnsorted);
+
+    /// Look up the name for a given SymbolId. UB if id is out of range.
+    [[nodiscard]] std::string_view getName(SymbolId id) const;
+
+    /// Look up full metadata for a SymbolId.
+    [[nodiscard]] const SymbolInfo& getInfo(SymbolId id) const;
+
+    /// Check if a symbol is a variable.
+    [[nodiscard]] bool isVariable(SymbolId id) const;
+
+    /// Number of interned symbols.
+    [[nodiscard]] size_t size() const;
+
+  private:
+    // TODO: Phase 1 implementation
+};
+
+}  // namespace atp
diff --git a/include/atp/core/term.h b/include/atp/core/term.h
new file mode 100644
index 0000000..e1edfcf
--- /dev/null
+++ b/include/atp/core/term.h
@@ -0,0 +1,43 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file term.h
+/// @brief Core Term data structure — hash-consed, immutable.
+
+#include <span>
+
+#include "atp/core/types.h"
+
+namespace atp {
+
+/// A term is a function/predicate application: f(t1, t2, ..., tn).
+/// Stored in a flat arena; args are contiguous TermIds following the header.
+/// Variables are represented as terms with a special symbol range.
+struct Term {
+    SymbolId symbol_id;  ///< Index into the SymbolTable
+    uint16_t arity;      ///< Number of arguments
+
+    /// Access the argument TermIds (stored immediately after this struct in the arena).
+    [[nodiscard]] std::span<const TermId> args() const;
+    [[nodiscard]] std::span<TermId> mutableArgs();
+};
+
+}  // namespace atp
diff --git a/include/atp/core/term_bank.h b/include/atp/core/term_bank.h
new file mode 100644
index 0000000..a121f8a
--- /dev/null
+++ b/include/atp/core/term_bank.h
@@ -0,0 +1,57 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file term_bank.h
+/// @brief Hash-consing term pool — guarantees structural sharing.
+
+#include "atp/core/term.h"
+#include "atp/core/types.h"
+
+#include <span>
+
+namespace atp {
+
+/// Global term pool with hash-consing.
+/// Every structurally identical term maps to the same TermId.
+class TermBank {
+  public:
+    TermBank() = default;
+
+    /// Create or retrieve a term. Returns the canonical TermId.
+    TermId makeTerm(SymbolId symbol, std::span<const TermId> args);
+
+    /// Create a variable term.
+    TermId makeVar(SymbolId var_symbol);
+
+    /// Look up a term by its ID.
+    [[nodiscard]] const Term& getTerm(TermId id) const;
+
+    /// Check if a TermId represents a variable.
+    [[nodiscard]] bool isVariable(TermId id) const;
+
+    /// Total number of unique terms stored.
+    [[nodiscard]] size_t size() const;
+
+  private:
+    // TODO: Phase 1 implementation — flat arena + hash index
+};
+
+}  // namespace atp
diff --git a/include/atp/core/types.h b/include/atp/core/types.h
new file mode 100644
index 0000000..c68e716
--- /dev/null
+++ b/include/atp/core/types.h
@@ -0,0 +1,80 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file types.h
+/// @brief Core type aliases for the ATP engine.
+
+#include <cstdint>
+
+namespace atp {
+
+/// Unique identifier for an interned symbol (predicate/function/constant name).
+using SymbolId = uint32_t;
+
+/// Unique identifier for a term in the Term Bank (hash-consed).
+using TermId = uint32_t;
+
+/// Unique identifier for a clause in the Clause Store.
+using ClauseId = uint32_t;
+
+/// Unique identifier for a sort/type (for sorted logic).
+using SortId = uint16_t;
+
+/// Sentinel value indicating an invalid / unassigned ID.
+inline constexpr uint32_t kInvalidId = UINT32_MAX;
+
+/// Default sort (unsorted logic).
+inline constexpr SortId kUnsorted = 0;
+
+/// Symbol kind — distinguishes variables from function/predicate symbols.
+enum class SymbolKind : uint8_t {
+    kVariable,   ///< Universally quantified variable
+    kConstant,   ///< 0-arity function symbol (constant)
+    kFunction,   ///< Function symbol (arity >= 1)
+    kPredicate,  ///< Predicate symbol (returns bool)
+    kSkolem,     ///< Skolem function/constant (introduced by Skolemization)
+};
+
+/// Inference rule that produced a clause.
+/// Deliberately uses uint16_t for extensibility toward algebra/analysis rules.
+enum class InferenceRule : uint16_t {
+    // ── Core resolution rules ──
+    kInput            = 0,    ///< Original input clause (axiom / negated conjecture)
+    kResolution       = 1,    ///< Binary resolution
+    kFactoring        = 2,    ///< Factoring
+
+    // ── Equality rules (algebra) ──
+    kParamodulation   = 100,  ///< Paramodulation (equality resolution)
+    kDemodulation     = 101,  ///< Demodulation (simplification by rewriting)
+    kEqualityResolution = 102, ///< s != t resolved with unifier
+    kEqualityFactoring  = 103, ///< Factoring with equality
+
+    // ── Simplification rules ──
+    kSubsumption      = 200,  ///< Removed by subsumption
+    kTautologyElim    = 201,  ///< Removed as tautology
+    kPureLiteralElim  = 202,  ///< Pure literal elimination
+
+    // ── Theory rules (analysis, arithmetic) ──
+    kTheoryResolution = 300,  ///< Theory-specific resolution
+    kTheoryRewrite    = 301,  ///< Theory-driven rewriting
+};
+
+}  // namespace atp
diff --git a/include/atp/frontend/tptp_parser.h b/include/atp/frontend/tptp_parser.h
new file mode 100644
index 0000000..f43f020
--- /dev/null
+++ b/include/atp/frontend/tptp_parser.h
@@ -0,0 +1,52 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file tptp_parser.h
+/// @brief Bridge from ANTLR4-generated parse tree to internal Formula AST.
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+#include "atp/normalize/formula.h"
+
+#include <string>
+#include <vector>
+
+namespace atp {
+
+/// Role of a TPTP formula (axiom, hypothesis, conjecture, etc.)
+enum class FormulaRole : uint8_t {
+    kAxiom,
+    kHypothesis,
+    kConjecture,
+    kNegatedConjecture,
+};
+
+/// A parsed TPTP formula with its name and role.
+struct AnnotatedFormula {
+    std::string name;
+    FormulaRole role;
+    std::unique_ptr<Formula> formula;
+};
+
+/// Parse a TPTP file and return the annotated formulas.
+std::vector<AnnotatedFormula> parseTptpFile(const std::string& filepath, TermBank& bank);
+
+}  // namespace atp
diff --git a/include/atp/index/discrim_tree.h b/include/atp/index/discrim_tree.h
new file mode 100644
index 0000000..8cadaa6
--- /dev/null
+++ b/include/atp/index/discrim_tree.h
@@ -0,0 +1,77 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file discrim_tree.h
+/// @brief Perfect Discrimination Tree for fast term indexing.
+///
+/// Used by subsumption and resolution to quickly find candidate clauses
+/// whose literals unify with a query term. Supports three query modes:
+///   - Unifiable:       find terms that can be unified with the query
+///   - Instances:       find terms that are instances of the query (more specific)
+///   - Generalizations: find terms that are generalizations of the query (more general)
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+#include "atp/core/types.h"
+
+#include <vector>
+
+namespace atp {
+
+/// A match result from the discrimination tree.
+struct IndexMatch {
+    ClauseId clause_id;
+    size_t lit_index;
+};
+
+/// A discrimination tree index over terms.
+/// Supports insertion and three types of retrieval queries.
+class DiscrimTree {
+  public:
+    explicit DiscrimTree(const TermBank& bank);
+
+    /// Insert a term (identified by its TermId) with an associated clause/literal ref.
+    void insert(TermId term, ClauseId clause_id, size_t lit_index);
+
+    /// Retrieve all entries whose indexed term is unifiable with `query`.
+    [[nodiscard]] std::vector<IndexMatch> queryUnifiable(TermId query) const;
+
+    /// Retrieve all entries whose indexed term is an instance of `query`.
+    /// (query is more general, indexed term is more specific)
+    [[nodiscard]] std::vector<IndexMatch> queryInstances(TermId query) const;
+
+    /// Retrieve all entries whose indexed term is a generalization of `query`.
+    /// (indexed term is more general, query is more specific)
+    /// This is the key operation for forward subsumption.
+    [[nodiscard]] std::vector<IndexMatch> queryGeneralizations(TermId query) const;
+
+    /// Remove all entries for a given clause.
+    void removeClause(ClauseId clause_id);
+
+    /// Number of indexed entries.
+    [[nodiscard]] size_t size() const;
+
+  private:
+    const TermBank& bank_;
+    // TODO: Phase 3 implementation — trie node arena
+};
+
+}  // namespace atp
diff --git a/include/atp/infer/resolution.h b/include/atp/infer/resolution.h
new file mode 100644
index 0000000..2d73b06
--- /dev/null
+++ b/include/atp/infer/resolution.h
@@ -0,0 +1,44 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file resolution.h
+/// @brief Binary resolution and factoring inference rules.
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+
+#include <optional>
+#include <vector>
+
+namespace atp {
+
+/// Attempt binary resolution between two clauses on the specified literal indices.
+/// @return The resolvent clause if resolution succeeds, std::nullopt otherwise.
+std::optional<Clause> resolve(const TermBank& bank, const Clause& c1, size_t lit_idx1,
+                              const Clause& c2, size_t lit_idx2);
+
+/// Generate all possible resolvents between two clauses.
+std::vector<Clause> allResolvents(const TermBank& bank, const Clause& c1, const Clause& c2);
+
+/// Attempt factoring on a single clause (merge two unifiable literals).
+std::vector<Clause> factor(const TermBank& bank, const Clause& c);
+
+}  // namespace atp
diff --git a/include/atp/infer/substitution.h b/include/atp/infer/substitution.h
new file mode 100644
index 0000000..f9f562a
--- /dev/null
+++ b/include/atp/infer/substitution.h
@@ -0,0 +1,54 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file substitution.h
+/// @brief Variable binding map: Var -> Term.
+
+#include "atp/core/types.h"
+
+#include <vector>
+
+namespace atp {
+
+/// A substitution is a mapping from variable TermIds to their bound TermIds.
+/// Designed as a short-lived, stack-allocated object during unification.
+class Substitution {
+  public:
+    Substitution() = default;
+
+    /// Bind a variable to a term. Returns false if already bound to something different.
+    bool bind(TermId var, TermId term);
+
+    /// Look up what a variable is bound to. Returns kInvalidId if unbound.
+    [[nodiscard]] TermId lookup(TermId var) const;
+
+    /// Walk the binding chain to the final bound value.
+    [[nodiscard]] TermId resolve(TermId id) const;
+
+    /// Clear all bindings.
+    void clear();
+
+  private:
+    // TODO: Phase 2 implementation
+    std::vector<std::pair<TermId, TermId>> bindings_;
+};
+
+}  // namespace atp
diff --git a/include/atp/infer/unification.h b/include/atp/infer/unification.h
new file mode 100644
index 0000000..7d91aaf
--- /dev/null
+++ b/include/atp/infer/unification.h
@@ -0,0 +1,40 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file unification.h
+/// @brief Most General Unifier (MGU) computation.
+
+#include "atp/core/term_bank.h"
+#include "atp/infer/substitution.h"
+
+namespace atp {
+
+/// Configuration for the unification algorithm.
+struct UnificationConfig {
+    bool enable_occurs_check = false;  ///< Set true for sound but slower unification
+};
+
+/// Attempt to unify two terms, producing a most general unifier.
+/// @return true if unification succeeds, with the MGU in `subst`.
+bool unify(const TermBank& bank, TermId t1, TermId t2, Substitution& subst,
+           const UnificationConfig& config = {});
+
+}  // namespace atp
diff --git a/include/atp/normalize/clausifier.h b/include/atp/normalize/clausifier.h
new file mode 100644
index 0000000..1ff4d27
--- /dev/null
+++ b/include/atp/normalize/clausifier.h
@@ -0,0 +1,38 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file clausifier.h
+/// @brief Converts FOL formulas to Clause Normal Form (CNF).
+///
+/// Pipeline: eliminate ↔/→  →  NNF  →  Skolemize  →  distribute ∨ over ∧  →  flatten.
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+#include "atp/normalize/formula.h"
+
+#include <vector>
+
+namespace atp {
+
+/// Convert a first-order formula into a set of clauses (CNF).
+std::vector<Clause> clausify(const Formula& formula, TermBank& bank);
+
+}  // namespace atp
diff --git a/include/atp/normalize/formula.h b/include/atp/normalize/formula.h
new file mode 100644
index 0000000..ccf1302
--- /dev/null
+++ b/include/atp/normalize/formula.h
@@ -0,0 +1,74 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file formula.h
+/// @brief First-order logic formula AST (pre-clausification).
+
+#include "atp/core/types.h"
+
+#include <memory>
+#include <string>
+#include <vector>
+
+namespace atp {
+
+/// AST node types for first-order logic formulas.
+enum class FormulaKind : uint8_t {
+    kAtom,       ///< Predicate application: P(t1, ..., tn)
+    kNot,        ///< Negation: ¬F
+    kAnd,        ///< Conjunction: F ∧ G
+    kOr,         ///< Disjunction: F ∨ G
+    kImplies,    ///< Implication: F → G
+    kIff,        ///< Biconditional: F ↔ G
+    kForall,     ///< Universal: ∀x. F
+    kExists,     ///< Existential: ∃x. F
+};
+
+/// A first-order logic formula node.
+struct Formula {
+    FormulaKind kind;
+
+    // For kAtom: the predicate term
+    TermId atom = kInvalidId;
+
+    // For quantifiers: the bound variable name
+    std::string var_name;
+
+    // Sub-formulas (1 for Not/Quantifiers, 2 for binary connectives)
+    std::vector<std::unique_ptr<Formula>> children;
+
+    static std::unique_ptr<Formula> makeAtom(TermId atom);
+    static std::unique_ptr<Formula> makeNot(std::unique_ptr<Formula> child);
+    static std::unique_ptr<Formula> makeAnd(std::unique_ptr<Formula> lhs,
+                                            std::unique_ptr<Formula> rhs);
+    static std::unique_ptr<Formula> makeOr(std::unique_ptr<Formula> lhs,
+                                           std::unique_ptr<Formula> rhs);
+    static std::unique_ptr<Formula> makeImplies(std::unique_ptr<Formula> lhs,
+                                                std::unique_ptr<Formula> rhs);
+    static std::unique_ptr<Formula> makeIff(std::unique_ptr<Formula> lhs,
+                                            std::unique_ptr<Formula> rhs);
+    static std::unique_ptr<Formula> makeForall(std::string var,
+                                               std::unique_ptr<Formula> body);
+    static std::unique_ptr<Formula> makeExists(std::string var,
+                                               std::unique_ptr<Formula> body);
+};
+
+}  // namespace atp
diff --git a/include/atp/proof/proof_trace.h b/include/atp/proof/proof_trace.h
new file mode 100644
index 0000000..cda6c5b
--- /dev/null
+++ b/include/atp/proof/proof_trace.h
@@ -0,0 +1,54 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file proof_trace.h
+/// @brief Proof reconstruction from the empty clause back to axioms.
+///
+/// This module depends only on ClauseStore (not Prover), so it can be
+/// reused with any search strategy.
+
+#include "atp/core/clause.h"
+#include "atp/core/clause_store.h"
+#include "atp/core/term_bank.h"
+
+#include <string>
+#include <vector>
+
+namespace atp {
+
+/// A single step in a reconstructed proof.
+struct ProofStep {
+    ClauseId clause_id;
+    InferenceRule rule;
+    ClauseId parent1;
+    ClauseId parent2;
+    std::string description;  ///< Human-readable description
+};
+
+/// Reconstruct the proof trace from the empty clause.
+/// Walks parent pointers via ClauseStore, independent of search strategy.
+std::vector<ProofStep> extractProof(const ClauseStore& store, ClauseId empty_clause_id,
+                                    const TermBank& bank);
+
+/// Format a proof as a human-readable string.
+std::string formatProof(const std::vector<ProofStep>& proof, const TermBank& bank);
+
+}  // namespace atp
diff --git a/include/atp/rewrite/ordering.h b/include/atp/rewrite/ordering.h
new file mode 100644
index 0000000..5696766
--- /dev/null
+++ b/include/atp/rewrite/ordering.h
@@ -0,0 +1,54 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file ordering.h
+/// @brief Term orderings for equality reasoning (KBO, LPO).
+///
+/// Term orderings are the foundation of equality-based theorem proving.
+/// They ensure that rewriting always terminates by enforcing a well-founded
+/// ordering on terms. Required by paramodulation, demodulation, and
+/// ordered resolution.
+
+#include "atp/core/term_bank.h"
+#include "atp/core/types.h"
+
+namespace atp {
+
+/// Ordering comparison result.
+enum class OrderResult : uint8_t {
+    kLessThan,       ///< t1 < t2
+    kEqual,          ///< t1 = t2
+    kGreaterThan,    ///< t1 > t2
+    kIncomparable,   ///< t1 and t2 are incomparable
+};
+
+/// Abstract base for term orderings.
+/// Concrete implementations: KBO (Knuth-Bendix), LPO (Lexicographic Path).
+class TermOrdering {
+  public:
+    virtual ~TermOrdering() = default;
+
+    /// Compare two terms under the ordering.
+    [[nodiscard]] virtual OrderResult compare(const TermBank& bank, TermId t1,
+                                              TermId t2) const = 0;
+};
+
+}  // namespace atp
diff --git a/include/atp/rewrite/paramodulation.h b/include/atp/rewrite/paramodulation.h
new file mode 100644
index 0000000..f43cd7b
--- /dev/null
+++ b/include/atp/rewrite/paramodulation.h
@@ -0,0 +1,48 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file paramodulation.h
+/// @brief Paramodulation inference rule for equality reasoning.
+///
+/// Paramodulation replaces a subterm in one clause with an equal term
+/// from an equation in another clause. Combined with term orderings,
+/// this gives a complete calculus for first-order logic with equality
+/// (the Superposition calculus).
+
+#include "atp/core/clause.h"
+#include "atp/core/term_bank.h"
+#include "atp/rewrite/ordering.h"
+
+#include <vector>
+
+namespace atp {
+
+/// Generate all paramodulants between two clauses.
+/// Uses the term ordering to restrict to ordered paramodulation (superposition).
+std::vector<Clause> paramodulate(const TermBank& bank, const Clause& c1, const Clause& c2,
+                                 const TermOrdering& ordering);
+
+/// Simplify a clause by demodulation (rewriting with unit equalities).
+/// Returns true if the clause was modified.
+bool demodulate(TermBank& bank, Clause& clause, const Clause& unit_eq,
+                const TermOrdering& ordering);
+
+}  // namespace atp
diff --git a/include/atp/search/clause_queue.h b/include/atp/search/clause_queue.h
new file mode 100644
index 0000000..828a725
--- /dev/null
+++ b/include/atp/search/clause_queue.h
@@ -0,0 +1,44 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file clause_queue.h
+/// @brief Priority queue for the Given Clause Loop.
+
+#include "atp/core/clause.h"
+
+#include <functional>
+
+namespace atp {
+
+/// Comparison function type for clause ordering.
+using ClauseComparator = std::function<bool(const Clause& a, const Clause& b)>;
+
+/// BFS comparator: prioritize shallower derivation depth.
+inline bool bfsCompare(const Clause& a, const Clause& b) {
+    return a.depth > b.depth;  // min-heap by depth
+}
+
+/// Weight comparator: prioritize shorter (fewer literals) clauses.
+inline bool weightCompare(const Clause& a, const Clause& b) {
+    return a.literals.size() > b.literals.size();  // min-heap by literal count
+}
+
+}  // namespace atp
diff --git a/include/atp/search/prover.h b/include/atp/search/prover.h
new file mode 100644
index 0000000..308e044
--- /dev/null
+++ b/include/atp/search/prover.h
@@ -0,0 +1,81 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file prover.h
+/// @brief The Given Clause Loop — main saturation-based proof search.
+///
+/// V1: Uses a simple ProverConfig with hardcoded resolution + factoring.
+/// V2: Will be refactored to accept a Calculus object from strategy/ module
+///     for dynamic algorithm loading per problem type.
+
+#include "atp/core/clause.h"
+#include "atp/core/clause_store.h"
+#include "atp/core/term_bank.h"
+#include "atp/search/clause_queue.h"
+
+#include <optional>
+#include <vector>
+
+namespace atp {
+
+/// Result of a proof attempt.
+enum class ProverResult : uint8_t {
+    kTheorem,       ///< Empty clause derived — conjecture is a theorem
+    kSaturation,    ///< Search space saturated — cannot prove
+    kTimeout,       ///< Resource limit exceeded
+};
+
+/// V1 configuration — simple and direct.
+/// Future: replaced by strategy::Calculus for dynamic rule loading.
+struct ProverConfig {
+    ClauseComparator comparator = bfsCompare;
+    size_t max_clauses = 100000;     ///< Safety limit
+    size_t max_iterations = 500000;  ///< Safety limit
+    bool enable_occurs_check = false;
+};
+
+/// Main prover class implementing the Given Clause Loop.
+/// V1: hardcodes resolution + factoring + subsumption.
+/// V2: will accept a Calculus object for pluggable inference rules.
+class Prover {
+  public:
+    Prover(TermBank& bank, ClauseStore& store, ProverConfig config = {});
+
+    /// Add initial clauses (axioms + negated conjecture).
+    void addClauses(std::vector<Clause> clauses);
+
+    /// Run the proof search.
+    ProverResult prove();
+
+    /// After a successful proof, retrieve the empty clause ID.
+    [[nodiscard]] std::optional<ClauseId> getEmptyClauseId() const;
+
+    /// Access the underlying clause store.
+    [[nodiscard]] const ClauseStore& clauseStore() const { return store_; }
+
+  private:
+    TermBank& bank_;
+    ClauseStore& store_;
+    ProverConfig config_;
+    // TODO: Phase 5 implementation — Unprocessed queue + Processed set
+};
+
+}  // namespace atp
diff --git a/include/atp/simplify/subsumption.h b/include/atp/simplify/subsumption.h
new file mode 100644
index 0000000..ee7a83e
--- /dev/null
+++ b/include/atp/simplify/subsumption.h
@@ -0,0 +1,55 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file subsumption.h
+/// @brief Forward and backward subsumption checks (backed by discrimination tree).
+
+#include "atp/core/clause.h"
+#include "atp/index/discrim_tree.h"
+
+#include <vector>
+
+namespace atp {
+
+/// Subsumption engine: checks if a new clause is subsumed by existing ones
+/// (forward) or subsumes existing ones (backward).
+class SubsumptionEngine {
+  public:
+    explicit SubsumptionEngine(const TermBank& bank);
+
+    /// Returns true if `candidate` is subsumed by any existing clause.
+    [[nodiscard]] bool isForwardSubsumed(const Clause& candidate) const;
+
+    /// Returns IDs of existing clauses that are subsumed by `new_clause`.
+    [[nodiscard]] std::vector<ClauseId> backwardSubsumed(const Clause& new_clause) const;
+
+    /// Add a clause to the subsumption index.
+    void addClause(const Clause& clause);
+
+    /// Remove a clause from the subsumption index.
+    void removeClause(ClauseId id);
+
+  private:
+    DiscrimTree index_;
+    // TODO: Phase 5 implementation
+};
+
+}  // namespace atp
diff --git a/include/atp/simplify/tautology.h b/include/atp/simplify/tautology.h
new file mode 100644
index 0000000..80aa1f9
--- /dev/null
+++ b/include/atp/simplify/tautology.h
@@ -0,0 +1,32 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file tautology.h
+/// @brief Tautology detection for clauses.
+
+#include "atp/core/clause.h"
+
+namespace atp {
+
+/// Returns true if the clause is a tautology (contains complementary literals).
+[[nodiscard]] bool isTautology(const Clause& clause);
+
+}  // namespace atp
diff --git a/include/atp/strategy/calculus.h b/include/atp/strategy/calculus.h
new file mode 100644
index 0000000..ee8ee09
--- /dev/null
+++ b/include/atp/strategy/calculus.h
@@ -0,0 +1,68 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file calculus.h
+/// @brief A Calculus bundles the exact set of inference rules + heuristics
+///        to use for a specific problem class.
+///
+/// Think of it as the "algorithm profile" that the Prover loads.
+/// Different problems get different calculi:
+///   - Pure propositional:  resolution + factoring only
+///   - FOL without equality: + full unification
+///   - FOL with equality:   + paramodulation + KBO ordering
+///   - Arithmetic:          + theory solver integration
+///
+/// This is the single point where search space control happens.
+
+#include "atp/rewrite/ordering.h"
+#include "atp/search/clause_queue.h"
+#include "atp/strategy/inference_rule.h"
+
+#include <memory>
+#include <string_view>
+#include <vector>
+
+namespace atp {
+
+/// A Calculus = a complete specification of how to search for a proof.
+/// The Prover is parameterized by this — it never hardcodes which rules to use.
+struct Calculus {
+    /// Name for logging (e.g., "superposition", "pure_resolution").
+    std::string name;
+
+    /// Generating rules (executed in order during the main loop).
+    std::vector<std::unique_ptr<GeneratingRule>> generating_rules;
+
+    /// Simplifying rules (applied to each new clause before enqueuing).
+    std::vector<std::unique_ptr<SimplifyingRule>> simplifying_rules;
+
+    /// Clause selection heuristic.
+    ClauseComparator comparator = bfsCompare;
+
+    /// Term ordering (nullptr if equality reasoning is disabled).
+    std::unique_ptr<TermOrdering> ordering = nullptr;
+
+    /// Resource limits.
+    size_t max_clauses = 100000;
+    size_t max_iterations = 500000;
+};
+
+}  // namespace atp
diff --git a/include/atp/strategy/inference_rule.h b/include/atp/strategy/inference_rule.h
new file mode 100644
index 0000000..1c7dbba
--- /dev/null
+++ b/include/atp/strategy/inference_rule.h
@@ -0,0 +1,81 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file inference_rule.h
+/// @brief Abstract interface for pluggable inference rules.
+///
+/// Each inference rule (resolution, factoring, paramodulation, etc.)
+/// is a self-contained object that the Prover can selectively load.
+/// This prevents search space explosion by only enabling rules relevant
+/// to the problem at hand.
+
+#include "atp/core/clause.h"
+#include "atp/core/clause_store.h"
+#include "atp/core/term_bank.h"
+
+#include <string_view>
+#include <vector>
+
+namespace atp {
+
+/// Abstract base class for all inference rules.
+/// The Prover invokes only the rules present in its active calculus.
+class InferenceRuleBase {
+  public:
+    virtual ~InferenceRuleBase() = default;
+
+    /// Human-readable name for logging and proof output.
+    [[nodiscard]] virtual std::string_view name() const = 0;
+
+    /// Is this a generating rule (produces new clauses) or simplifying rule
+    /// (rewrites/deletes existing clauses)?
+    enum class Kind : uint8_t { kGenerating, kSimplifying };
+    [[nodiscard]] virtual Kind kind() const = 0;
+};
+
+/// Generating inference rule: given a "given clause" and the set of processed
+/// clauses, produce new clauses.
+class GeneratingRule : public InferenceRuleBase {
+  public:
+    [[nodiscard]] Kind kind() const final { return Kind::kGenerating; }
+
+    /// Generate new clauses from the given clause against all processed clauses.
+    /// @param given     The selected clause from the Unprocessed queue.
+    /// @param processed All previously processed clauses (accessed via store).
+    /// @param bank      The global term bank.
+    /// @return Newly generated clauses (not yet added to the store).
+    [[nodiscard]] virtual std::vector<Clause> generate(
+        const Clause& given, const std::vector<ClauseId>& processed,
+        const ClauseStore& store, TermBank& bank) const = 0;
+};
+
+/// Simplifying inference rule: rewrite or delete a clause in-place.
+class SimplifyingRule : public InferenceRuleBase {
+  public:
+    [[nodiscard]] Kind kind() const final { return Kind::kSimplifying; }
+
+    /// Attempt to simplify a clause. Returns true if the clause was modified.
+    /// If the clause should be deleted entirely, clear its literals.
+    virtual bool simplify(Clause& clause, const ClauseStore& store,
+                          TermBank& bank) const = 0;
+};
+
+}  // namespace atp
diff --git a/include/atp/strategy/problem_analyzer.h b/include/atp/strategy/problem_analyzer.h
new file mode 100644
index 0000000..b5fdef4
--- /dev/null
+++ b/include/atp/strategy/problem_analyzer.h
@@ -0,0 +1,62 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file problem_analyzer.h
+/// @brief Analyzes input clauses and selects the optimal Calculus.
+///
+/// Before the Prover starts its main loop, the ProblemAnalyzer inspects
+/// the input clause set to determine problem characteristics:
+///   - Contains equality?             → enable paramodulation
+///   - Pure Horn clauses?             → use SLD resolution
+///   - Contains arithmetic literals?  → enable theory solver
+///   - Problem size / clause density  → tune resource limits
+///
+/// This is the "auto mode" that mature ATPs use to avoid loading
+/// unnecessary inference rules that would explode the search space.
+
+#include "atp/core/clause.h"
+#include "atp/strategy/calculus.h"
+
+#include <vector>
+
+namespace atp {
+
+/// Features detected in the input problem.
+struct ProblemFeatures {
+    bool has_equality = false;        ///< Contains '=' predicate
+    bool is_purely_propositional = false;  ///< No function symbols, no variables
+    bool is_horn = false;             ///< All clauses are Horn clauses
+    bool has_existential = false;     ///< Had existential quantifiers (Skolemized)
+    size_t num_clauses = 0;
+    size_t num_predicates = 0;
+    size_t num_functions = 0;
+    size_t max_clause_size = 0;
+    size_t max_term_depth = 0;
+};
+
+/// Analyze the input clauses and extract problem features.
+ProblemFeatures analyzeFeatures(const std::vector<Clause>& clauses, const TermBank& bank);
+
+/// Select the optimal calculus based on detected features.
+/// This is the core strategy dispatch logic.
+std::unique_ptr<Calculus> selectCalculus(const ProblemFeatures& features);
+
+}  // namespace atp
diff --git a/include/atp/utils/hash_utils.h b/include/atp/utils/hash_utils.h
new file mode 100644
index 0000000..4531fa6
--- /dev/null
+++ b/include/atp/utils/hash_utils.h
@@ -0,0 +1,47 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file hash_utils.h
+/// @brief Hash combination utilities.
+
+#include <cstddef>
+#include <cstdint>
+#include <functional>
+
+namespace atp {
+
+/// Combine a hash with a new value (boost::hash_combine style).
+inline void hashCombine(size_t& seed, size_t value) {
+    seed ^= value + 0x9e3779b9 + (seed << 6) + (seed >> 2);
+}
+
+/// Hash a span of values.
+template <typename T>
+size_t hashRange(const T* data, size_t count) {
+    size_t seed = 0;
+    std::hash<T> hasher;
+    for (size_t i = 0; i < count; ++i) {
+        hashCombine(seed, hasher(data[i]));
+    }
+    return seed;
+}
+
+}  // namespace atp
diff --git a/include/atp/utils/logger.h b/include/atp/utils/logger.h
new file mode 100644
index 0000000..95d3dd2
--- /dev/null
+++ b/include/atp/utils/logger.h
@@ -0,0 +1,43 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
+#pragma once
+
+/// @file logger.h
+/// @brief Minimal high-performance logging macros.
+
+#include <cstdio>
+
+#ifndef ATP_LOG_LEVEL
+#define ATP_LOG_LEVEL 2  // 0=TRACE, 1=DEBUG, 2=INFO, 3=WARN, 4=ERROR
+#endif
+
+#define ATP_LOG(level, level_str, fmt, ...)                        \
+    do {                                                           \
+        if constexpr (level >= ATP_LOG_LEVEL) {                    \
+            std::fprintf(stderr, "[%s] " fmt "\n", level_str,     \
+                         ##__VA_ARGS__);                           \
+        }                                                          \
+    } while (0)
+
+#define ATP_TRACE(fmt, ...) ATP_LOG(0, "TRACE", fmt, ##__VA_ARGS__)
+#define ATP_DEBUG(fmt, ...) ATP_LOG(1, "DEBUG", fmt, ##__VA_ARGS__)
+#define ATP_INFO(fmt, ...)  ATP_LOG(2, "INFO",  fmt, ##__VA_ARGS__)
+#define ATP_WARN(fmt, ...)  ATP_LOG(3, "WARN",  fmt, ##__VA_ARGS__)
+#define ATP_ERROR(fmt, ...) ATP_LOG(4, "ERROR", fmt, ##__VA_ARGS__)
diff --git a/src/core/clause_store.cc b/src/core/clause_store.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/core/clause_store.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/core/symbol_table.cc b/src/core/symbol_table.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/core/symbol_table.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/core/term_bank.cc b/src/core/term_bank.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/core/term_bank.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/frontend/tptp_parser.cc b/src/frontend/tptp_parser.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/frontend/tptp_parser.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/index/discrim_tree.cc b/src/index/discrim_tree.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/index/discrim_tree.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/infer/resolution.cc b/src/infer/resolution.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/infer/resolution.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/infer/unification.cc b/src/infer/unification.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/infer/unification.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/main.cc b/src/main.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/main.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/normalize/clausifier.cc b/src/normalize/clausifier.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/normalize/clausifier.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/proof/proof_trace.cc b/src/proof/proof_trace.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/proof/proof_trace.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/rewrite/ordering.cc b/src/rewrite/ordering.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/rewrite/ordering.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/rewrite/paramodulation.cc b/src/rewrite/paramodulation.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/rewrite/paramodulation.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/search/prover.cc b/src/search/prover.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/search/prover.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/simplify/subsumption.cc b/src/simplify/subsumption.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/simplify/subsumption.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/src/strategy/problem_analyzer.cc b/src/strategy/problem_analyzer.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/src/strategy/problem_analyzer.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
new file mode 100644
index 0000000..d841595
--- /dev/null
+++ b/tests/CMakeLists.txt
@@ -0,0 +1,27 @@
+# ─── GoogleTest ───────────────────────────────────────────────────────────────
+include(FetchContent)
+FetchContent_Declare(
+    googletest
+    GIT_REPOSITORY https://github.com/google/googletest.git
+    GIT_TAG        v1.14.0
+)
+# Prevent GoogleTest from overriding our compiler/linker options
+set(gtest_force_shared_crt ON CACHE BOOL "" FORCE)
+FetchContent_MakeAvailable(googletest)
+
+include(GoogleTest)
+
+# ─── Helper: define a test target ────────────────────────────────────────────
+function(atp_add_test TEST_NAME TEST_SOURCE)
+    add_executable(${TEST_NAME} ${TEST_SOURCE})
+    target_link_libraries(${TEST_NAME} PRIVATE atp_core GTest::gtest_main)
+    gtest_discover_tests(${TEST_NAME})
+endfunction()
+
+# ─── Test Targets ────────────────────────────────────────────────────────────
+atp_add_test(test_term_bank       test_term_bank.cc)
+atp_add_test(test_unification     test_unification.cc)
+atp_add_test(test_clausifier      test_clausifier.cc)
+atp_add_test(test_resolution      test_resolution.cc)
+atp_add_test(test_discrim_tree    test_discrim_tree.cc)
+atp_add_test(test_prover          test_prover.cc)
diff --git a/tests/test_clausifier.cc b/tests/test_clausifier.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/tests/test_clausifier.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/tests/test_discrim_tree.cc b/tests/test_discrim_tree.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/tests/test_discrim_tree.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/tests/test_prover.cc b/tests/test_prover.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/tests/test_prover.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/tests/test_resolution.cc b/tests/test_resolution.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/tests/test_resolution.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/tests/test_term_bank.cc b/tests/test_term_bank.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/tests/test_term_bank.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+
diff --git a/tests/test_unification.cc b/tests/test_unification.cc
new file mode 100644
index 0000000..b62ffd0
--- /dev/null
+++ b/tests/test_unification.cc
@@ -0,0 +1,19 @@
+/*
+ * richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
+ * Copyright (C) 2026 Richard Qin
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+